ELECTRONIC and OPTICAL PROPERTIES of Tis2 DETERMINED from MODIFIED BECKE–JOHNSON GGA POTENTIAL (Mbj-GGA) STUDY

ACADEMIA ROMÂNĂ Rev. Roum. Chim., Revue Roumaine de Chimie 2018, 63(10), 873-880

http://web.icf.ro/rrch/

ELECTRONIC AND OPTICAL PROPERTIES OF TiS2 DETERMINED FROM MODIFIED BECKE–JOHNSON GGA POTENTIAL (mBJ-GGA) STUDY

Hamza EL-KOUCH and Larbi EL FARH*

Mechanics and Energetic Laboratory, Faculty of Sciences, University Mohammed 1st, Oujda, Morocco

Received May 2, 2017

In this study, we report the results of electronic structure and optical properties of TiS2 calculations within the density functional theory (DFT) using the generalized gradient approximation (GGA) and an improved version of the modified Becke-Johnson (mBJ) exchange- correlation potential. The equilibrium lattice parameters and bulk modulus were found to be close to the experimentally reported results and a semi-conducting character of the material was revealed from the band structure calculation with an indirect band gap of 0.26 eV. Furthermore, DOS plots showed a prominent contribution of Ti-d, S-s and S-p. We have also calculated the dielectric function, refractive index and optical reflectivity and we have compared the obtained curves to those found experimentally by other authors.

INTRODUCTION* there are many conflicting results on the electronic structure of TiS2, since it is still debated whether the Recent progress in material sciences has shown material is metallic, semi-metallic or semiconductor.8- 12 that the dimensionality of materials plays a crucial Several experimental works have reported that TiS2 role in determining their fundamental properties.1 has semiconductor behavior with a band gap ranging Especially, the two-dimensional materials, like the from 0.05 to 2.5 eV.8-10 At the same time, other 11 12 graphene, have shown rich physical properties not works classify TiS2 among metals or semi-metals observed in bulk or in the one-dimensional materials. with an indirect band gap overlap (between the points For this reason, in the latest years the properties of Γ and L in the first Brillouin zone). other 2D materials like transition-metal The aim of the present paper is to investigate dichalcogenides (TMDs) have known a renewal of the electronic, structural and optical properties of interest due to their potential applications in next- TiS2 using density functional theory (DFT) and full 2 generation nanoelectronic devices. The titanium potential linearized and augmented plane wave disulfide (TiS2) is one of those materials; it consists (FLAPW) basis set. of covalently bonded Ti and S atoms arranged in two-dimensional hexagonal planes.3 The layers are stacked together by weak Van Der Waals forces.4 COMPUTATIONAL METHODS TiS2 has been widely studied in recent years because of its use in numerous applications, particularly as a The calculations presented in this paper have cathode material in rechargeable batteries,5 as been performed within the framework of density hydrogen storage material,6 and as a high- functional theory (DFT) using the full-potential performance thermoelectric material.7 In literature, linearized augmented plane wave (FP-LAPW)

* Corresponding author: [email protected]; Phone: +212628378953. 874 Hamza El-Kouch et al. method13 as implemented in the Wien2K code.14 The modified Becke-Johnson potential (mBJ) The mBJ potential for the exchange correlation as proposed by Tran and Blaha16 is: potential15 was used to calculate electronic and optical properties.

1 5 2t (r) V mBJ ()r = CV BR + (3C − 2 ) σ (1) X ,σ X ,σ π 12 ρ ()r σ where C is a system-dependent parameter, with BR energy density and VX ,σ ()r is the Becke-Roussel C = 1 corresponding to the original BJ 17 N 2 (BR) potential given by: potential, ρ = σ ψ is the electronic σ ∑i=1 i,σ

 1  Nσ ∗ density, tσ =   ∇ψ i,σ ∇ψ i,σ is the kinetic  2 ∑i=1

BR 1  − X ()r 1 − X ()r  V ()r = − 1− e σ − X ()r e σ  (2) X ,σ b r 2 σ σ () 

BR 1 VX ,σ ()r was originally proposed to mimic the 3 − Xσ 3  X σ e  Slater potential, the Coulomb potential bσ is calculated by: bσ =   . corresponding to the exact exchange hole.  8πρσ 

X σ is determined from an equation involving ρσ , In eq. (1), parameter C was proposed by Tran and Blaha16, for bulk crystalline materials, by the ∇ρ , ∇ 2 ρ and t . σ σ σ following empirical relation:

1 '  1 ∇ρ()r  2 C = −0.012 +1.023   (3)  ∫cell ' 3 '  Vcell ρ()r d r   where Vcell is the volume of the unit cell. Brillouin zone for k-space integration to achieve Larger C values than 1 lead to a less negative self-consistency. (less attractive) potential, in particular, in low- density regions. In the FP-LAPW method, a unit cell is divided RESULTS AND DISCUSSION into an interstitial zone and non-interweaving spheres known as muffin-tin (MT) of a specific 1. Structural Properties radius (RMT). Inside the MT spheres, the basis The titanium disulfide TiS has a layered sets are described by a linear combination of radial 2 hexagonal structure with space group P-3m1 (No. solutions of Schrödinger equation (for a single 164).15 One Ti atom is located at 1a (0, 0, 0) and particle and at fixed energy) along with the energy two S atoms at 2d (1/3, 2/3, 1/4) and (2/3, 1/3, 3/4) derivatives time spherical harmonics. Inside each in the unit cell, as shown in Figure 1. MT sphere, the set of basis is divided into subsets The lattice parameters and all atomic positions (core and valence). The spherically symmetric within a crystal unit cell have been relaxed in order to charge density core subsets are completely reach equilibrium configuration. The relaxation was confined inside the MT sphere. The muffin-tin radii performed simulating the XC effects by generalized RMT were chosen equal to 2.34 for Ti and 2.08 Å gradient approximation (GGA) with Perdew, Burke and Ernzerhof (PBE) parameterization. Electronic for S. The RMT*Kmax parameter was taken equal to 9. To ensure the correctness of our calculations, we structure and optical calculations were then have taken l = 10 and G = 12. Also, in the performed on this, fully relaxed structure simulating max max the XC effects by modified Becke-Johnson. This self-consistent calculations, we consider that the choice has been made due to that it has been total energy is converged to within 0.1 mRy. Note demonstrated16 that the mBJ provides a better that we have used 900 K-points in the first description of the band gaps and optical properties. Electronic and optical properties of TiS2 875

Fig. 1 – Unit cell of TiS2.

Table 1 Structural parameters derived from Murnaghan-Birch equation of state 3 a (Å) b (Å) c (Å) V0[Å ] B0[GPa] B0’ E0[Ry] Present work 3.31 3.31 5.55 59.10 95.6281 4.2432 -3304.704936 Experiment 3.40718 3.40718 5.69518 57.244 45.904 9.504 Other works 51.724 58.914 4.114

In the present work the TiS2 structure was fully of S is also observed below the Fermi energy in the optimized, i.e. the lattice parameters and all the region from -5 to 0 eV. atomic positions were relaxed in order to reach the The band structure of TiS2 was calculated with values that correspond to energy minimum. The theoretical lattice parameters obtained in the results are presented in Table 1. previous section. This gait makes sense in the It is clearly seen that our lattice constant results context of a self-consistent first principle close to the experimental values with a small calculation and allows to compare the theoretical overestimation while an underestimation of bulk results at experience. The electronic band structure modulus is observed, that can be attributed to the calculated along the lines of symmetry of the general trend of PBE-GGA method which usually Brillouin zone (Figure 3) is presented in Figure 4. overestimates the lattice constant. The bulk Like for all semiconductors, they are characterized modulus (B0) is a measure of how resistant to by a band gap between the conduction band and compressibility that substance is, thus a large value the valence band. The minimum of the conduction of B0 indicates high crystal rigidity. band is located at L point and the maximum of the valence band is located at Γ point of the first 2. Electronic Properties Brillouin zone. This permits us to conclude that TiS2 is a semiconductor with indirect gap equal to To determine the nature of the electronic band 0.26 eV, which is not far of the experimental value structure, we calculated the density of states (DOS) of 0.3 eV.8 of TiS2. Thus, figure 2 shows the total and partial density of states obtained by mBJ-GGA for TiS . 2 3. Optical Properties From total DOS in Figure 2(a), we can distinguish, in the valence band, two separate In this part, we will present some optical regions. The first region, the valence lowest energy properties like dielectric function, refractive index, is due to S s-orbitals as is indicated in figure 2 (b). reflectivity, optical conductivity and absorption The second region is separated from the first by 6.7 because those calculations play a vital role in the eV. It is dominated by the Ti d and S-p orbitals in profound understanding of the nature of the the figure 2(b). Lowest conduction region located material. All these properties can be calculated above the Fermi level is formed mainly of states d from the complex dielectric function: of Ti atom with low contribution of states p of S atom. The second conduction region is separated ε(ω) = ε1(ω) + i ε2(ω) (4) from the first by 2.4 eV. It is dominated by the Ti-d where ε (ω) and ε (ω) are respectively the real and states and S-p. The existence of a very strong 1 2 the imaginary parts of the dielectric function. hybridization between the d states of Ti and p states

876 Hamza El-Kouch et al.

Fig. 2 – (a) Total and (b) Partial Density of state for TiS2 within mBJ-GGA.

Fig. 3 – Brillouin zone and high-symmetry points for TiS2.

Fig. 4 – (a) Electronic band structures and (b) Partial electronic density of states of TiS2. Electronic and optical properties of TiS2 877

Fig. 5 – (a) Real part of dielectric function ε1(ω), (b) Imaginary part of dielectric function ε2(ω). Experimental values are dashed.19

This function allows describing the linear The figure 5b shows calculated and experimental response of the system to excitation by an incident plot of imaginary part ε2(ω) of the dielectric function electromagnetic radiation. for TiS2. From those curves, we can distinguish In figures 5(a) and 5(b), we compare the curves 3 peaks: (A) at around 1.9 eV, for both experimental obtained by calculation and experimentally, of and calculated curves, (B) at around 4 eV, for both respectively the real and imaginary parts of the experimental and calculated curves and (C) at around dielectric function as a function of the energy of 9 eV for experimental curve and at around 10.5 for that calculated. The imaginary part ε2(ω) of the photon for TiS2. The real part of the dielectric function ε (ω) dielectric function is related to the absorption 1 spectrum due to the electronic transitions from the gives us information about the electronic valence band to conduction band. By comparing the polarizability of the material. The imaginary part peaks which appear in figure 5(b) with the figure 2 of ε2(ω) is directly associated to the electronic band the DOS, it is possible to deduce between which structure, and this last can be calculated by adding orbitals these transitions are made. Thus, it can be all possible occupied states to the unoccupied recognized that the peaks A, B and C in figure 5(b) states of transitions. are mainly due to transitions from S-p valence bands The static dielectric constant at zero is to Ti-d conduction bands. At a higher energy, the ε1(0) = 17.5, but the experimental value is equal to spectrum is without structures and decays very 30. From its zero frequency, the real part of the rapidly as function of the energy of photon. dielectric function ε1(ω) increases in function of The optical reflectivity is one of the most the energy and at 0.8 eV reaches the maximum important parameters in optical calculations. In value of 22.6 for calculated curve and 35.1 for the fact, reflectivity is responsive to a complicated experimental. After, there is a dip in the amplitude combination of ε1(ω) and ε2(ω). This is generally of the real part of dielectric function and it attains a described by the portion of the light energy minimum negative value at 2 eV for experimental reflected from the material surface. In figure 6(a), we have displayed the frequency dependent curve and at 2.2 eV for that calculated indicating reflectivity R(ω). that there is plasmonic excitation near 2 eV. Also, Calculated and experimental reflectivity spectra dip in ε1(ω) at around 4.5 for experimental curve of TiS2 consist of three main, strong bands with and at around 5.1 for that calculated indicate several fine structures superimposed. The first two plasmon excitation. 878 Hamza El-Kouch et al. bands, centered at about 2 eV and 5 eV, are The optical conductivity as function of approximately 2 and 3 eV wide. The third one having frequency for TiS2 calculated with mBJ-GGA is a better shape in experimental curve is centered at shown in the figure 7(a). His behavior follows that about 10.8 eV and is also approximately 3 eV wide. of the imaginary part of the dielectric function

Our calculated spectra differ from experimental ε2(ω), since those two quantities are proportional. ones essentially for the relative intensities of the The energy loss function L(ω) calculated with peaks, in the interval 0.6 - 12 eV. mBJ-GGA is displayed in Figure 7(b). This Figure 6 (b) shows the calculated absorption function L(ω) is an important factor describing the coefficient as a function of the frequency using energy loss during the fast electron traversing in a mBJ-GGA method. Similar features are observed material. The peaks in L(ω) spectra represent the in absorption coefficient in the absorption range up characteristic associated with the plasma to 14 eV, it also shows three structures as in ε1(ω), resonance. The resonant energy loss is seen at ε2(ω) and R(ω). about 8 eV.

Fig. 6 – (a) Reflectivity spectrum R(ω), (b) Absorption coefficient α(ω). Experimental values are dashed.20

Fig. 7 – Frequency dependent (a) Optical conductivity σ(ω) (b) Energy-loss spectrum L(ω). Electronic and optical properties of TiS2 879

Fig. 8 – Refractive index n(ω) of TiS2 within mBJ-GGA.

The calculated refractive index n(ω) for TiS2 the optical parameters of the compound. We have compound in range of energy (0 –14 eV) is found that TiS2 has a semiconductor character with depicted in Figure 8. We observe the optically indirect gap of about 0.26 eV, which is in very anisotropic nature of this compound. The refractive close agreement to the experimental result of 0.3 index spectrum n(ω) follows the real part of the eV. The achieved structural properties, with an dielectric function ε1(ω) because it is closely optimization using PBE-GGA, are in suitable linked to this latter. The calculated refractive index agreement with other found theoretical and experimental works. We have calculated the at zero frequency for TiS2 is found to be equal approximately to 4.2. The refractive index n(ω) frequency dependent dielectric functions and we found considerable anisotropy. The frequency spectrum of TiS2 shows two significant features. First, a maximum is observed in the spectrum at dependent dielectric functions show three main about 0.9 eV, in infrared range. When the structures arising primarily from band transitions refractive index is greater than one, photons from the chalcogen p valence states to the Ti-d conduction states. We have also calculated the entering in material are slowed down by their frequency dependent reflectivity and the interactions with electrons. The more photons are absorption coefficient. Calculated static dielectric slowed down while travelling through the material, constant static refractive index and coefficient of the greater is the refractive index. Generally, any reflectivity at zero frequency for TiS within mBJ- mechanism that increases electron density in a 2 GGA are also presented. material also increases its refractive index. Secondly, the refractive index of TiS2 goes below one, between 6.3 eV and 8.3 eV. REFERENCES

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